Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class Solution {
    static class FastReader {   
        BufferedReader br;
        StringTokenizer st;

        public FastReader(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        float nextFloat() {
            return Float.parseFloat(nextToken());
        }
    }


    static FastReader f = new FastReader();
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static StringBuilder sb = new StringBuilder();
    static long[] fact;

    static int[] inputArray(int n) throws IOException {
        int[] a = new int[n];
        for(int i = 0 ; i < n ; i++) {
//            a[i] = (int) (Math.random()*1e5 + 1);
            a[i] = f.nextInt();
        }
        return a;
    }

    static void print2DArray(int[][] a) {
        int n = a.length, m = a[0].length;
        for(int i = 0 ; i < n ; i++) {
            for(int j = 0 ; j < m ; j++) {
                System.out.print(a[i][j] + " ");
            }
            System.out.println();
        }

    }

    static void print2DArray(long[][] a) {
        int n = a.length, m = a[0].length;
        for(int i = 0 ; i < n ; i++) {
            for(int j = 0 ; j < m ; j++) {
                System.out.print(a[i][j] + " ");
            }
            System.out.println();
        }

    }

    static long[] inputLongArray(int n) throws IOException {
        long[] a = new long[n];
        for(int i = 0 ; i < n ; i++) {
            a[i] = f.nextLong();
//            a[i] = (long) (Math.random() * 1e9 + 1);
        }
        return a;
    }

    static long gcd(long a , long b) {
        if(a == 0 || b == 0) {
            return Math.max(a , b);
        }
        //System.out.println("a - " + a + " b - " + b);
        if(a % b == 0) {
            return b;
        }
        return gcd(b , a % b);
    }

    static void initializeFact() {
        fact = new long[MAX_N];
        for(int i = 0 ; i < fact.length ; i++) {
            if(i == 0) {
                fact[i] = 1;
            }
            else {
                fact[i] = fact[i-1] * i % mod;
            }
        }
    }

    static long longModulus(long x , long m) {
        if(x < m) {
            return x;
        }
        long d = x / m;
        return x - d * m;
    }


    static BitSet sieveOfEratosthenes(int n)
    {
        BitSet isPrime = new BitSet(n+1);
        isPrime.set(0, n + 1);
        isPrime.set(0);
        isPrime.set(1);
        for(int i = 2; i * i <= n ; i++)
        {
            if(isPrime.get(i))
                for(int j = i * i ; j <= n; j += i)
                    isPrime.clear(j);
        }
        return isPrime;
    }

    static long moduloInversePrime(long a) {
        //System.out.println("modulo inverse of " + a + " -> " + ans);
        return modPow(a , mod - 2);
    }

    static long mult(long a, long b)
    {
        return (a * b % mod);
    }

    static long modPow(long a, int step)
    {
        long ans = 1;
        while(step != 0)
        {
            if((step & 1) != 0)
                ans = mult(ans , a);
            a = mult(a , a);
            step >>= 1;
        }
        return ans;
    }

    static int query(int l , int r) {
        System.out.println("? " + l + " " + r);
        System.out.flush();
        return f.nextInt();
    }


    private static int mod = (int) (1e9 + 7);
    static int MAX_N = (int) Math.sqrt(1e9);


    static long getPreSum(long[] presum, int i) {
        if(i == -1) {
            return 0;
        }
        return presum[i];
    }

    static void addToMap(Map<Long, Long> map, long i) {
        if(map.containsKey(i)) {
            map.replace(i, map.get(i) + 1);
        }
        else {
            map.put(i, 1l);
        }
    }

    static void removeFromMap(Map<Long, Long> map, long i) {
        if(map.containsKey(i)) {
            map.replace(i, map.get(i) - 1);
        }
        if(map.get(i) == 0) {
            map.remove(i);
        }
    }

    public static void main(String[] args) throws IOException {
        int n = f.nextInt();
        int[] a = inputArray(n);
        int s = 0;
        for(int x: a) s += x;
        if(s % 2 == 1) {
            System.out.println(0);
        }
        else {
            int half = s/2;
            boolean[][] dp = new boolean[n+1][half + 1];
            for(int i = 0 ; i <= n ; i++) {
                dp[i][0] = true;
            }
            for(int i = 1 ; i <= n ; i++) {
                for(int j = 1 ; j <= half ;j++) {
                    dp[i][j] = dp[i-1][j];
                    if(j - a[i-1] >= 0) {
                        dp[i][j] |= dp[i-1][j-a[i-1]];
                    }
                }
            }
            if(dp[n][half]) {
                System.out.println(1);
                boolean got = true;
                while(got) {
                    for(int i = 0 ; i < n ; i++) {
                        if((a[i] & 1) == 1) {
                            System.out.println((i + 1));
                            got = false;
                            break;
                        }
                        else {
                            a[i] = a[i] >> 1;
                        }
                    }
                }
            }
            else {
                System.out.println(0);
            }
        }
    }
}